Trump-Kim summit has concluded on a happy note, with United States Donald Trump calling his meeting with North Korean leader Kim Jong Un "really fantastic", a historic event in Singapore that came after decades of hostility.

"A lot of progress, really very positive, better than anybody could have expected," said Trump as he stood beside Kim after their meetings. "Top of the line. Really good."

The summit marked the basic stage in a process that the U.S., Japan, China and South Korea hope will lead to denuclearization on the Korean peninsula. In order to discuss the negotiations, Trump was scheduled to hold a press conference at 4 p.m. local time.

As the two men walked through the Capello Hotel where the summit was held, Kim said to Trump that "many people in the world will think of this as a form of fantasy from a science fiction movie." Trump added that the two men would head to a "signing" ceremony without providing any details.

Following one-on-one meeting for about 40 minutes, before holding a working lunch, they met with their broader delegations.

The U.S. delegation comprised of secretary of state Mike Pompeo, National security adviser John Bolton and Chief of staff John Kelly whereas the North Korean side included Kim's confidant Kim Yong Chol, who recently met Trump in the White House.

At the beginning of the summit, Kim said there would be "challenges ahead but we will work with President Trump". He said, "We overcame all kinds of skepticism and speculations about this summit and I believe that this is good for the peace."

Moon Jae-in, the South Korean president, on Tuesday, hoped that the summit would bring "complete denuclearization and peace, and open a new era for the South, the North, and the U.S."

"The fact that I am having a meeting is a major loss for the U.S., say the haters and losers. We have our hostages, testing, research and all missile [sic] launches have stopped [sic], and these pundits, who have called me wrong from the beginning, have nothing else they can say! We will be fine!" Trump said before leaving his downtown hotel for the Capella.

Security was tight across Singapore and peculiarly near the Capella. The White House said Trump would hold a press conference at 4 p.m. local time in Singapore, where several thousand journalists have poured into the city-state to cover the historic event.

The U.S. said little regarding the talk terms leading up to the summit. Merely it has stressed that North Korea would remain under sanctions until it undertook the "complete, verifiable and irreversible denuclearization" of the Korean peninsula. In return, it has offered to render security guarantees, which Pyongyang desperately wants.

"We are prepared to take what will be security assurances that are different, unique than . America has been willing to provide previously. We think this is both necessary and appropriate," said Pompeo, who refused to say whether the guarantees would include removing the more than 28,000 US troops stationed in South Korea.